Fourth order 4-stages improved Runge-Kutta method with minimized error norm

Faranak Rabiei, Fudziah Ismail

Research output: Chapter in Book/Report/Conference proceedingConference PaperOther

1 Citation (Scopus)


In this paper the improved Runge-Kutta method of order four with 4-stages for solving first order ordinary differential equation is proposed. The method is based on classical Runge-Kutta (RK) method also can be considered as special class of two-step method. Here, the coefficients of the method are obtained using the minimization of the error norm up to order five. The improved method with only 4-stages is more accurate than fourth order 4-stages RK method. Therefore it is computationally more efficient than the existing RK method. A number of test problems are solved and the numerical results compared with the existing RK method are given.

Original languageEnglish
Title of host publicationStatistics and Operational Research International Conference, SORIC 2013
EditorsLai Soon Lee, Mahendran Shitan, Zainidin K. Eshkuvatov
PublisherAmerican Institute of Physics
Number of pages6
ISBN (Electronic)9780735412491
Publication statusPublished - 2014
Externally publishedYes
EventStatistics and Operational Research International Conference 2013 - Sarawak, Malaysia
Duration: 3 Dec 20135 Dec 2013

Publication series

NameAIP Conference Proceedings
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616


ConferenceStatistics and Operational Research International Conference 2013
Abbreviated titleSORIC 2013


  • Improved Runge-Kutta method
  • Minimization of error norm
  • Ordinary differential equations
  • Two-step method

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